Is "føles" is more like a sensation and "kjennes" is like a perception?
"å kjenne" can mean 1) to know, 2) to sense, 3) to try, 4) to judge.
"å føle" can mean 1) to examine using touch, 2) to notice, 3) to experience.
As a swedish speaker I guessed kjennes=felt. How would you say felt? Kjennet?
What is the difference between 'kjennes' and 'kjenner'? Is it like with 'treffer' and 'treffes', depending on the presence of an object? If so, is it like that with all the -es forms of verbs?
The "-s" is used for three different things: making a verb reflexive (i.e. the subject is also the object), making it reciprocal (i.e. multiple subjects with each other as objects) and for constructing the passive voice. In this case it is the last one. The person feeling the dream is nowhere in the sentence.